Robotics Fundamentals
Robot Configurations and Workspaces
The five classic arm layouts (Cartesian, cylindrical, spherical, SCARA and articulated) plus parallel robots. And the reachable workspace each geometry carves out of space.
beginner · 14 min read
Lesson content
Almost every robot arm ever built is one of about five shapes. That is not a coincidence.
The first three joints decide where the hand can go. And there are only so many sensible ways to stack a sliding joint and a turning joint three times over.
Each combination has a name. Each one carves a different solid shape out of the air around the robot.
Definition
Configuration
The pattern of joint types in the first three joints of an arm, which is the part that positions the wrist in space. Written as letters: R for a revolute (turning) joint, P for a prismatic (sliding) joint.
Formal definition
The kinematic arrangement of the major (positioning) axes of a manipulator, conventionally denoted by the ordered sequence of joint types, e.g. RRR for an articulated arm or PPP for a Cartesian gantry.
Read the letters left to right, starting at the floor and working outward. R is a joint that rotates. P is one that slides, from prismatic.
PPP is three sliders, so the hand moves in straight lines only, like a 3D printer.RRR is three hinges, so everything turns and the reachable volume becomes a fat lopsided ball.
Anything beyond those first three joints is the wrist. The wrist sets which way the tool points rather than where it is.
| Configuration | Joints | Workspace shape | Typical job |
|---|---|---|---|
| Cartesian / gantry | PPP | Rectangular box | 3D printing, pick-and-place over a table, CNC |
| Cylindrical | RPP | Hollow cylinder | Machine loading, spot welding around one post |
| Spherical / polar | RRP | Thick spherical shell | Older welding and casting arms (Unimate) |
| SCARA | RRP (vertical axis) | Flat annular ring, thick | Fast flat assembly, PCB insertion |
| Articulated | RRR | Lopsided ball | Almost everything: welding, painting, packing |
Cartesian / gantry
- Joints
- PPP
- Workspace shape
- Rectangular box
- Typical job
- 3D printing, pick-and-place over a table, CNC
Cylindrical
- Joints
- RPP
- Workspace shape
- Hollow cylinder
- Typical job
- Machine loading, spot welding around one post
Spherical / polar
- Joints
- RRP
- Workspace shape
- Thick spherical shell
- Typical job
- Older welding and casting arms (Unimate)
SCARA
- Joints
- RRP (vertical axis)
- Workspace shape
- Flat annular ring, thick
- Typical job
- Fast flat assembly, PCB insertion
Articulated
- Joints
- RRR
- Workspace shape
- Lopsided ball
- Typical job
- Almost everything: welding, painting, packing
- Cartesian (gantry)
Three sliders at right angles, like the axes of a graph.
Dead simple maths, because a target of (x, y, z) is the joint command. Very stiff and very accurate, but the frame has to be bigger than the work area.
- Cylindrical
A turning base, a vertical slider and an arm that slides in and out.
Reaches all the way around a post without a large frame. The dead zone in the middle is the column itself.
- Spherical (polar)
A turning base, a shoulder that tilts and an arm that extends.
The layout of the very first industrial robot. Long reach for its size, but hard to keep stiff when fully extended.
- SCARA
Selective Compliance Assembly Robot Arm: two horizontal hinges plus a vertical slider.
Stiff straight down and springy sideways, which is exactly right for pushing a part into a hole. The fastest configuration for flat assembly work.
- Articulated
Shoulder, elbow and base all hinges. The human-arm layout.
The most flexible reach per unit of floor space, which is why roughly three of every four industrial arms are this shape.
Definition
Workspace (work envelope)
Every point in space the robot's tool can physically reach. Not a marketing number but a solid shape, with holes in it.
Formal definition
The set of all positions attainable by the end-effector's reference point given the joint limits of the manipulator. The reachable workspace contains every attainable point; the dexterous workspace contains only points attainable in any orientation.
Why does the workspace have a hole in the middle?
Because links have length and joints have stops.
An articulated arm cannot fold its forearm back through its own shoulder. So there is a ball of space right beside the base that it can never touch. A cylindrical arm cannot reach inside its own column.
Every real workspace is a shell or a lopsided blob with dead zones in it.
Here is the practical consequence and it catches people out constantly. A fixture placed too close to the base is just as unreachable as one placed too far away.
The workspace comes in two grades and mixing them up ruins layouts.
The reachable workspace is everywhere the tool can get to at all, even if it has to arrive at an awkward angle.
The dexterous workspace is the smaller region inside it where the tool can reach a point and still be aimed any way you like.
Which one you need depends on the job. A gluing nozzle that must stay vertical everywhere needs the dexterous workspace. A simple pick that only has to touch a point is happy with the reachable one.
All five layouts above are serial chains: one link bolted to the next, base to hand, like a human arm. There is a second family that works the opposite way round.
| Serial (open chain) | Parallel (closed chain) | |
|---|---|---|
| Shape | One chain: base → link → link → hand | Several chains from base to one platform |
| Example | Any 6-axis industrial arm | Delta picker, Stewart platform, flight simulator |
| Workspace | Large | Small |
| Stiffness / payload | Lower, because errors add up along the chain | Much higher, because the load is shared by every leg |
| Speed | Moderate, since heavy motors move with the arm | Very high, since the motors sit on the fixed base |
| Forward kinematics | Easy | Hard |
| Inverse kinematics | Hard | Easy |
Shape
- Serial (open chain)
- One chain: base → link → link → hand
- Parallel (closed chain)
- Several chains from base to one platform
Example
- Serial (open chain)
- Any 6-axis industrial arm
- Parallel (closed chain)
- Delta picker, Stewart platform, flight simulator
Workspace
- Serial (open chain)
- Large
- Parallel (closed chain)
- Small
Stiffness / payload
- Serial (open chain)
- Lower, because errors add up along the chain
- Parallel (closed chain)
- Much higher, because the load is shared by every leg
Speed
- Serial (open chain)
- Moderate, since heavy motors move with the arm
- Parallel (closed chain)
- Very high, since the motors sit on the fixed base
Forward kinematics
- Serial (open chain)
- Easy
- Parallel (closed chain)
- Hard
Inverse kinematics
- Serial (open chain)
- Hard
- Parallel (closed chain)
- Easy
Example
Why a delta robot can pick 200 items a minute
In a delta robot, all three motors are bolted to the ceiling frame and never move.
The only things that actually accelerate are three feather-light carbon rods and a small platform. The arm has almost no weight of its own to throw around.
Now picture an ordinary articulated arm doing the same job. Every single move has to fling its own elbow motor along for the ride.
Same electrical power, wildly different acceleration. That is the whole bargain a parallel robot makes: hand back workspace, buy speed and stiffness.
Choosing a configuration from the task
Sketch the work volume, not the robot
Where must the tool actually go? A flat tray at one height, a tall rack, the inside of a car body? The shape of that volume is the first filter.
Ask what orientations you need
Tool always pointing down? Two or three axes are plenty. Tool at arbitrary angles, such as welding a curved seam and you need six.
Check payload and cycle time together
Heavy and slow favours a stiff serial arm or a hydraulic one. Light and blisteringly fast favours SCARA or delta.
Then look at floor space
A gantry needs a frame larger than its work area. An articulated arm needs a small footprint but a large sphere of clearance. Both are constraints on the room rather than on the robot.
Reading “reach: 900 mm” as “can reach any point within 900 mm”.
That number is the maximum radius on one particular plane. Ask the vendor for the work-envelope diagram. The real shape always has bites taken out of it.
Buying a 6-axis arm for a job where the tool only ever points straight down.
A SCARA or a delta will do that job faster, cheaper and with simpler maths. Extra axes you never use are cost, mass and failure modes you pay for forever.
Assuming more degrees of freedom always means more capable.
Beyond six, extra joints buy you the ability to reach around obstacles rather than to reach more places. That is genuinely useful, but it is a different benefit.
Key takeaway
- The first three joints set position. The wrist joints set orientation.
- Five classic serial layouts: Cartesian (PPP), cylindrical (RPP), spherical (RRP), SCARA and articulated (RRR).
- Each configuration sweeps a characteristic workspace: a box, a cylinder, a shell, a ring or a lopsided ball, always with dead zones.
- Reachable workspace is “can the tool touch it”. Dexterous workspace is “can it touch it at any angle”.
- Parallel robots trade a small workspace for stiffness and speed, then swap which kinematics problem is the hard one.
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